Gary Tupper says:>Which makes difficult any attempt to draw the model of a Real line as distinct from a Rational or Irrational line.

Might as well rely on the old symbols R and Q to differentiate. I vaguely remember the Rs were generally not ordinary Rs, but had a funny double vertical line on the left. Maybe the Qs had that funny doubling too ... no doubt very significant ;-) Anyway, its not hard to add an R or a Q to the picture.